Page 118 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

dy
Unit 6: Existence Theorem for the Solution of the Equation = f(x, y)
dx

6.6 Keyword Notes

The method of finding the conditions for the existence of the solution of the first order differential
equation is quite appealing but sometimes cumbersome.

6.7 Review Questions

dy
1. Solve x y .
dx
when x = 0, y = 1, by Picard method up to fifth successive approximation

dy 2
2. Solve  3x  y
dx
given x = 0, y = 1.
up to third successive approximation.
Answers: Self-Assessment

x 2 x 3 x 4
1. y = 1 x ......
2 3 4
x n
= .
n
n 0
1 2 1 5 1 8 1 11
2. y = x x x x .
2 20 160 4400
6.8 Further Readings

Books Yosida, K., Lectures in Differential and Integral Equations

Piaggio, H.T.H., Differential Equations

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